Newt Gingrich (Jemal Countess/GETTY IMAGES FOR TIME)

“Parks and Rec,” of course, is the NBC sitcom that, just last month, featured Veep Joe Biden playing himself. What are the odds?

The restaurant does not open until 4 p.m., the restaurant’s marketing guy told ABC News on Tuesday.

But, the marketing guy said, the doors were “wide open” because of the shoot.  Which, if you’ve ever been at a TV show location shoot, is pretty much par for the course — doors wide open and the welcome mat out.

Anyway, while Gingrich mistook all the trucks and TV producing equipment for lunchtime customers at a popular restaurant, the writers and producers who were there for the shoot, sat down and slapped together a short scene in which Gingrich would play himself.

You buying any of this?

“It was great fun,” Gingrich told ABC News, explaining he’s “intrigued by American entertainment,” and adding, “Always fun to do something like that” — like the old sitcom pro he is.

In case ABC News had forgotten, he reminded them, “I had a small role on a Candice Bergen show many years back.”

That “Candice Bergen show” was CBS’s controversial sitcom “Murphy Brown” — controversial because the Washington journalist Brown, played by Bergen, was an unwed mother. And, back in ’92, then Veep Dan Quayle condemned the fictitious characters’ made-for-TV unwed motherhood, during one of those family-values debates to which Washington is prey.

Four years later, in February of ’96, then House Speaker Newt Gingrich played himself on the show, in a scene in which he confronted Murphy Brown backstage after she skewered Gingrich at a Washington "Presscapade" dinner — (think Gridiron dinner).

“That was quite a speech,” said an unusually generous Gingrich.

“Oh, really?” Murphy responded. "There were some people who thought that writing ‘Newt' on a greased pig went a little too far."

“Oh, I can take a little ribbing,” Gingrich responded, adding that the First Amendment applies even to journalists like her.

Speaker of the House Newt Gingrich appears with Candice Bergen Tuesday, Feb. 6, 1996, in Burbank, Calif., (SPIKE NANNARELLO/AP)

At the time, The Post’s Sharon Waxman complained of Gingrich’s “Murphy Brown” taping,  “they promised viewers a rumble, but it was more like a romp.”

“Ever since I saw ‘The Wind and the Lion’ I said I go to any length to be in the same room” with Candice Bergen, gushed Gingrich after the taping.

“He did it so quickly; he’s a natural talent,” cooed Bergen.

Gingrich was stiff on the first take, Waxman reported, but was relaxed and confident by Take 5, even improvising with a carrot, which he bit into as he told an aide to “look into” revising the First Amendment — which he’d foozled earlier, calling it “the Last Amendment.”

After the taping, Bergen handed Gingrich a souvenir show baseball cap and T-shirt, saying “We’re trying to keep it amiable, in re the taping chumminess.

“Hey, we're not doing ‘Crossfire,’ Gingrich jumped in, insisting, “Lots of people watch ‘Murphy Brown' because they like the show, not necessarily because they like the ideology.”

He declined the T-shirt, saying it is banned under the no-gifts rule he helped push through Congress. The hat, he said, qualified as a "memento" — an interpretation he admitted to having invented on the spot, Waxman reported.